Due to their light-weight and cost-effectiveness, cellular thermoplastic foams are considered as important engineering materials. On the other hand, additive manufacturing or 3D printing is one of the emerging and fastest growing manufacturing technologies due to its advantages such as design freedom and tool-less production. Nowadays, 3D printing of polymer compounds is mostly limited to manufacturing of solid parts. In this context, a merged foaming and printing technology can introduce a great alternative for the currently used foam manufacturing technologies such as foam injection molding. This perspective review article tackles the attempts taken toward initiating this novel technology to simultaneously foam and print thermoplastics. After explaining the basics of polymer foaming and additive manufacturing, this article classifies different attempts that have been made toward generating foamed printed structures while highlighting their challenges. These attempts are clustered into 1) architected porous structures, 2) syntactic foaming, 3) post-foaming of printed parts, and eventually 4) printing of blowing agents saturated filaments. Among these, the latest approach is the most practical route although it has not been thoroughly studied yet. A filament free approach that can be introduced as a potential strategy to unlock the difficulties to produce printed foam structures is also proposed.